Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11549 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#13303 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#99 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C22×Q8 | C23×C11 |
| prime radical | C23×C11 | C2×C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×Q8×C11 ◁ G | |
396 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,18)(15,16)(17,19)(20,21,25,29,26,30,23,27)(22,31,33,24,28,32,35,34);(13,16)(17,18)(20,22,32,29,26,28,31,27)(21,25,35,24,30,23,33,34);(12,14,15,19)(13,17,16,18)(20,23,26,25)(21,27,30,29)(22,33,28,35)(24,32,34,31)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6291);